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%I #9 May 21 2018 08:48:14
%S 0,594,9898,67852,293464,955602,2567334,6003816,12643728,24534258,
%T 44579634,76753204,126333064,200161234,306926382,457470096,665116704,
%U 946026642,1319573370,1808743836,2440562488,3246538834,4263138550
%N Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two or three adjacent elements summing to zero.
%C Row 4 of A200430.
%H R. H. Hardin, <a href="/A200434/b200434.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical: a(n) = (5887/180)*n^6 - (5813/60)*n^5 + (6083/36)*n^4 - (2191/12)*n^3 + (9119/90)*n^2 - (353/15)*n.
%F Conjectures from _Colin Barker_, May 21 2018: (Start)
%F G.f.: 2*x^2*(297 + 2870*x + 5520*x^2 + 2784*x^3 + 303*x^4) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=3:
%e ..0...-3....3....2...-2....1....2...-1....3....0...-1....0...-2....2...-1....1
%e .-3....0....2...-1....3....0....3...-2....3....1...-2...-2...-2...-1....0....1
%e .-1....2...-1....2....0....1...-2...-3...-1....2...-2....1...-1....3....2....0
%e ..2....0...-3....0....2....3....0....0...-3....1....3....3...-1....3....1...-3
%e ..1....2....2...-1....1...-2....1....1....1...-2....1....2....3...-2....0...-3
%e ..1....1....0...-1...-2...-2...-3....3...-3...-3....3...-1....0...-3...-3....1
%e ..0...-2...-3...-1...-2...-1...-1....2....0....1...-2...-3....3...-2....1....3
%Y Cf. A200430.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 17 2011
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